We develop a theory for a continuous bandwidth-tuned transition at fixed fractional electron filling from a metal with a generic Fermi surface to a "Wigner-Mott"insulator that spontaneously breaks crystalline space-group symmetries. Across the quantum critical point, (i) the entire electronic Fermi surface disappears abruptly upon approaching from the metallic side, and (ii) the insulating charge gap and various order parameters associated with the spontaneously broken space-group symmetries vanish continuously upon approaching from the insulating side. Additionally, the insulating side hosts a Fermi surface of neutral spinons. We present a framework for describing such continuous metal-insulator transitions (MITs) and analyze the example of a bandwidth-tuned transition at a filling, ν=1/6, for spinful electrons on the triangular lattice. By extending the theory to a certain large-N limit, we provide a concrete example of such a continuous MIT and discuss numerous experimental signatures near the critical point. We place our results in the context of recent experiments in moiré transition metal dichalcogenide materials. © 2022 American Physical Society.